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Numbers System — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumbers System2 Marks
Question
Simplify: $\Bigg(\frac{12^\frac{1}{5}}{27^\frac{1}{5}}\Bigg)^\frac{5}{2}$
✓

Answer

$\Bigg(\frac{12^\frac{1}{5}}{27^\frac{1}{5}}\Bigg)^\frac{5}{2}$$=\frac{12^{\frac{1}{5}\times\frac{5}{2}}}{15^{\frac{1}{5}\times\frac{5}{2}}}$
$=\frac{12^\frac{1}{2}}{27^\frac{1}{2}}$
$=\frac{\sqrt{12}}{\sqrt{27}}$
$=\frac{\sqrt{4\times3}}{\sqrt{9\times3}}$
$=\frac{2\sqrt3}{3\sqrt3}$
$=\frac{2}{3}$

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